Thanks for the observations and direction, Ted.
Since I only want my machines set up logged, the DAW would remember the sysex data from my BK and anything else plugged in would ignore it. Hence the "exclusive" in "sysex".
And because it is just data, the DAW would happily record it, even if it did not know what it meant. But, as you say, this does not seem possible.
I shall explore better the section in the manual on "User Programs" and try to do as you advise.